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Find the vertex, focus and directrix of the parabola `4y^2+12 x-12 y+39=0.`

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To find the vertex, focus, and directrix of the parabola given by the equation \(4y^2 + 12x - 12y + 39 = 0\), we will follow these steps: ### Step 1: Rearrange the equation We start by rearranging the equation to group the \(y\) terms and \(x\) terms together: \[ 4y^2 - 12y + 12x + 39 = 0 \] ...
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RD SHARMA-PARABOLA-Solved Examples And Exercises
  1. The focal distance of a point on the parabola y^2=12 x is 4.Find the ...

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  2. Find the equation of the parabola whose focus is at (-2) and the dir...

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  3. Find the vertex, focus and directrix of the parabola 4y^2+12 x-12 y+39...

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  4. Find the angle made by a double ordinate of length at the vertex of th...

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  5. P is parabola, whose vertex and focus are on the positive x axis at di...

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  6. Find the locus of the middle points of the chords of the parabola y^2=...

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  7. If a parabolic reflector is 20 cm in diameter and 5 cm deep, find its ...

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  8. over the towers of a bridge a cable is hung in the form of a parabola,...

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  9. An arch is in the form of a parabola with its axis vertical. The arc i...

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  10. A beam is supported at its ends by supports which are 12 metres apart....

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  11. Find the equation of the parabola whose: focus is (3,0) and the dir...

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  12. The equation of the parabola whose focus is (1, 1) and the directrix ...

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  13. Find the equation of the parabola whose: focus is (0,0) and the dir...

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  14. Find the length of the latus rectum of the parabola whose focus is at ...

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  15. Find the length of the latus rectum of the parabola whose focus is at ...

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  16. Find the equation of the parabola, if the focus is at (-6,-6) and the...

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  17. Find the equation of the parabola, if: the focus is at (0,-3) and the ...

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  18. Find the equation of the parabola, if: the focus is at (a ,0) and the ...

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  19. Find the equation of the parabola whose focus is (0,0) and the vertex ...

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  20. Find the vertex , focus, axis, directrix and latus rectum of the fo...

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